   Chapter 8.1, Problem 48E ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

#### Solutions

Chapter
Section ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
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# Arc Length In Exercises 47-50, use the following information, as shown in the figure. For a circle of radius r, a central angle θ (in radians) intercepts an arc of length s given by s = r θ . Distance A tractor tire that is 5 feet in diameter is partially filled with a liquid ballast for additional traction. To check the air pressure, the tractor operator rotates the tire until the valve stem is at the top so that the liquid will not enter the gauge. On a given occasion, the operator notes that the tire must be rotated 80 ° to have the stem in the proper position (see figure). What is the radius of the tractor tire?Find the radian measure of this rotation.How far must the tractor be moved to get the valve stem in the proper position?

(a)

To determine

To calculate: The radius of tractor tire if the tractor tire of diameter 5 ft is rotated 80°.

Explanation

Given Information:

A 5 ft diameter tractor tire is partially filled with liquid ballast. In order to check the air pressure, the tire is rotated until the valve stem is at the top. To bring the stem in proper position, the tire is rotated at an angle of 80°.

The figure provided below shows the tractor tire.

Formula used:

The radius of a circle is,

r=d2

Where, d is the diameter of a circle

(b)

To determine

To calculate: The rotation of the tire in radians if the tractor tire of diameter 5 ft is rotated 80°.

(c)

To determine

To calculate: The distance moved by tractor to get the value stem into the proper position if a 5 ft diameter tractor tire is rotated at an angle of 80° in order to bring the stem in proper position. In order to check the air pressure, the tire is rotated until the valve stem is at the top. The tire partially filled with liquid ballast.

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